The results in this section are for \(T = 50\)  REs, \(N_s = 10^3\)  Monte Carlo runs, \(\lambda = 10^{-2}\) , \(\alpha = 3.76\) , \(\sigma _h^2 = 1\) , SINR threshold \(\gamma _{\text{th}} = 10\) , MSBL threshold \(\gamma _{\text{pr}} = 10^{-6}\) , cell radius \(r_{\max } = 1000\)  m, and reference distance \(r_0 = 100\)  m [1]}.
The number of users contending for the \(T\)  REs is computed based on the load \(L\)  as \(M = \lfloor L T \rceil \) .
The soliton distribution [2]} with \( d_{\max } = 27 \)  maximum repetitions is used to generate the repetition factor \(d_m\)  for the \(m\) th user, whose access pattern is formed by uniformly randomly choosing \(d_m\)  REs from \(T\)  REs [3]}.
The APM is formed by stacking the pattern vectors of all the users.
The location of each user is uniformly sampled from within a cell of radius \(r_{\max }\)  centered at the BS.
The path loss coefficient is calculated as \(\beta _m = (r_m/r_0)^{-\alpha }\)  where \(r_m\)  is the radial distance of the \(m\) th user from the BS.
The signal to noise ratio (SNR) for the \(m\) th user is calculated as \(P \sigma _h^2\beta _m/N_0\) .
The received SNR of a user at the edge of the cell at the BS is termed as the cell edge SNR, and is denoted by \(\text{SNR}_{\text{edge}}\) .
The power levels of all users is chosen such that the signal from a user at a distance \(r_{\max }\)  from the BS is received at \(\text{SNR}_{\text{edge}}\) .
This ensures that all users' signals are received at an SINR that at least \(\text{SNR}_{\text{edge}}\)  on average, in singleton REs.
If \(\text{SNR}_{\text{edge}} \ge \gamma _{\text{th}}\) , i.e., it is such that the cell edge user's signal is decodable, then all users' signals are decodable with high probability in singleton REs.
The power levels of users is set to \(P =P_{\tau } =20\)  dBm [1]} and \(N_0\)  is chosen such that the cell edge SNR is 10 dB, unless otherwise stated.
The pilot sequence for each user is generated as \(\mathbf {p}_m \sim \mathcal {CN}(\mathbf {0}_{\tau }, P_\tau \mathbf {I}_{\tau } )\) .
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